Structural mechanisms and the thermodynamic description of the isosymmetric orbital ordering in rare-earth manganites

The observed specific features of the orbital phase transition in AMnO$_3$ (A = La, Pr, $\dots$, Lu) are shown to be due to the appearance, at high temperatures, of rotational distortions of the cubic lattice, which cause anion displacements, which induce an “internal field” coinciding in symmetry with the order parameter, which describe the ordering of octahedra distorted due to the Jahn–Teller effect (orbital ordering). The effect of this “field” substantially determines the orbital ordering type, its temperature, and the phase transition order. The comparative analysis of the orbitally ordered states is performed for the entire AMnO$_3$ series in both the framework of the phenomenological theory of phase transitions and on the base of the three-minimum multi-sublattice model proposed in this report. The peculiarities of magnetic transitions in manganites determined by the specific features of their structures are discussed.